The invention is based on an anti-skid brake system and anti-drive-slip system as generally defined hereinafter. A system of this type known from U.S. Pat. No. 4,589,706, has a pressure supply apparatus; a valve actuated by the brake pedal for controlling brake pressures; a sensing piston coupled with the brake valve for sensing brake pressures controlled by means of the valve; a booster piston, a master cylinder, which is actuatable by the booster piston and to which cylinder brake circuits including anti-skid valves and wheel brakes are connected; and a change-over valve assembly for feeding pressure from the valve that is actuatable by means of the brake pedal into the brake circuits, in order to reestablish brake pressures after brake pressure reductions have been effected in order to lessen the danger of skidding. The change-over valve assembly is additionally embodied such that upon the appearance of undesirable drive slip, pressure medium from the pressure supply apparatus is fed into the brake circuits, bypassing the valve that is actuable by means of the brake pedal. This system has the advantage that only the pressures that are controlled by means of the brake pedal act upon the sensing piston; that is, brake pressures having the purpose of reducing drive slip do not produce any feedback upon the brake pedal. The disadvantage, however, is that all the brake circuits are embodied as so-called openable brake circuits, and for safety reasons expensive monitoring equipment is therefore required. Furthermore, between brake line junctions where feeding is performed and the master cylinder, blocking valves are required, and in the event of anti-drive-slip operation these must be closed. These blocking valves further complicate the system and raise its price.